Aiza is a name of Basque Spanish origin and means cliff or rock. Aiza is a spelling variation on Arista, or in Basque, Aritza
Aydhah and Aayedhah are two names with the same meaning, which could be spelled and pronounced as Aizah, Ayza, Ayeza and Aayza mean "replacement" and "substitute", something good that Allah gives us as a gift in replacement for something we lost.
Ayza is pronounced as p(AY) + (Z) + r(U)n
Ayeza is pronounced as (EYE) + (Z) + r(U)n or (EYE) + (YI)eld + (Z) + r(U)n
Since the meaning is good inshAllah you can use it. The name is not from the Quran, but it is Arabic and used by Muslims, so it can be considered an Islamic name.